Quantum-mechanical Lorentzian wormholes in cosmological backgrounds

We present a minisuperspace analysis of a class of Lorentzian wormholes that evolves quantum mechanically in a background Friedmann-Robertson-Walker spacetime. The quantum-mechanical wave function for these wormholes is obtained by solving the Wheeler-DeWitt equation for Einstein gravity on this minisuperspace. The time-dependent expectation value of the wormhole throat radius is calculated to lowest order in an adiabatic expansion of the Wheeler-DeWitt Hamiltonian. For a radiation-dominated expansion, the radius is shown to relax asymptotically to obtain a value of order the Planck length while for a de Sitter background the radius is stationary but always larger than the Planck length. These two cases are of particular relevance when considering wormholes in the early universe.